Finally, from a manipulation of the integral by substitution, the obtained function can be written in the form of an incomplete elliptic integral of the third kind [1]}.
\(\psi (t) = \frac{G}{I_{z}}t - \frac{G(I_{x} - I_{z})}{I_{x}I_{z}n} \text{\Large $\Pi $}\left(\text{am}(nt + \tau ) ,\;-\tfrac{I_{z}(I_{x} - I_{y})}{I_{x}(I_{y} - I_{z})},\;k\right) + \Lambda \) 
